The Geometrization of Physics
by Richard S. Palais
Publisher: University of California at Irvine 1981
Number of pages: 107
The major goal of these notes is to develop, in sufficient detail to be convincing, an observation that basically goes back to Kaluza and Klein in the early 1920's that not only can gauge fields of the "Yang-Mills" type be unified with the remarkable successful Einstein model of gravitation in a beautiful, simple, and natural manner, but also that when this unification is made they, like gravitational field, disappear as forces and are described by pure geometry, in the sense that particles simply move along geodesics of an appropriate Riemannian geometry.
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by Alain Connes, Matilde Marcolli - American Mathematical Society
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.
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From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.
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